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This page offers a straightforward tutorial on the fundamentals of vector operations. It is an illustrated guide to vector subtraction/addition, vector resolution, and multiplication of two vectors. It could serve as textbook supplementation or as content support for science teachers.

Standards (7)

Common Core State Standards for Mathematics Alignments

High School — Number and Quantity (9-12)

Vector and Matrix Quantities (9-12)

N-VM.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).

N-VM.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

N-VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.

N-VM.4.a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

N-VM.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

N-VM.4.c Understand vector subtraction v — w as v + (—w), where —w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

Citation Formats

<a href="http://www.compadre.org/portal/items/detail.cfm?ID=7754">Department of Physics, University of Guelph. Guelph Physics Tutorials: Vectors. Guelph: Department of Physics, University of Guelph, March 29, 2006.</a>

Department of Physics, University of Guelph. Guelph Physics Tutorials: Vectors. Guelph: Department of Physics, University of Guelph, March 29, 2006. http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html (accessed 31 March 2015).

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